Csomós, Petra and Faragó, István and Fekete, Imre (2015) Numerical stability for nonlinear evolution equations. COMPUTERS AND MATHEMATICS WITH APPLICATIONS. ISSN 0898-1221
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Abstract
The paper deals with discretisation methods for nonlinear operator equations written as abstract nonlinear evolution equations. Brezis and Pazy showed that the solution of such problems is given by nonlinear semigroups whose theory was founded by Crandall and Liggett. By using the approximation theorem of Brezis and Pazy, we show the N-stability of the abstract nonlinear discrete problem for the implicit Euler method. Motivated by the rational approximation methods for linear semigroups, we propose a more general time discretisation method and prove its N-stability as well. © 2015 Elsevier Ltd.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Nonlinear equations; Rational approximations; Nonlinear operator equations; Nonlinear evolution equation; Non-linear stabilities; Implicit Euler method; Discretisation method; Approximation theorem; STABILITY; Mathematical operators; Differential equations; Chaos theory; Approximation theory; Nonlinear stability; Nonlinear semigroups; Nonlinear rational approximations |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 02 Oct 2015 12:18 |
| Last Modified: | 02 Oct 2015 12:18 |
| URI: | http://real.mtak.hu/id/eprint/29429 |
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